A262047 - OEIS

%I #10 Feb 15 2017 11:14:52

%S 0,0,2,6,66,510,4280,46536,542962,7074654,101914512,1621871196,

%T 28087868160,526841965260,10641234260358,230278335503586,

%U 5315641087796562,130370690653563150,3385534274596691456,92801584815121975452,2677687776095609649256

%N Number of ordered partitions of [n] such that at least two parts have the same size.

%C All terms are even.

%H Alois P. Heinz, <a href="/A262047/b262047.txt">Table of n, a(n) for n = 0..424</a>

%F a(n) = A000670(n) - A032011(n).

%p g:= proc(n) option remember; `if`(n<2, 1,

%p        add(binomial(n, k)*g(k), k=0..n-1))

%p     end:

%p b:= proc(n, i, p) option remember;

%p       `if`(i*(i+1)/2<n, 0, `if`(n=0, p!, b(n, i-1, p)+

%p       `if`(i>n, 0, b(n-i, i-1, p+1)*binomial(n, i))))

%p     end:

%p a:= n-> g(n)-b(n$2, 0):

%p seq(a(n), n=0..25);

%t g[n_] := g[n] = If[n<2, 1, Sum[Binomial[n, k]*g[k], {k, 0, n-1}]]; b[n_, i_, p_] := b[n, i, p] = If[i*(i+1)/2<n, 0, If[n==0, p!, b[n, i-1, p] + If[i>n, 0, b[n-i, i-1, p+1]*Binomial[n, i]]]]; a[n_] := g[n] - b[n, n, 0]; Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Feb 15 2017, translated from Maple *)

%Y Cf. A000670, A032011, A262046, A261982.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Sep 09 2015